The pole of the straight line $x + 2y = 1$ with respect to the circle $x^2 + y^2 = 5$ is

The polar of the origin $(0, 0)$ with respect to the circle ${x^2} + {y^2} + 2\lambda x + 2\mu y + c = 0$ touches the circle ${x^2} + {y^2} = {r^2}$,if

If $2x - 3y + 3 = 0$ and $x + 2y + k = 0$ are conjugate lines with respect to the circle $S \equiv x^2 + y^2 + 8x - 6y - 24 = 0$,then the length of the tangent drawn from the point $\left(\frac{k}{4}, \frac{k}{3}\right)$ to the circle $S = 0$ is

The locus of the poles of the tangents to the circle $x^2+y^2-2x+2y-2=0$ with respect to the circle $x^2+y^2=4$ is:

The pole of the line $x-5y-7=0$ with respect to the circle $S \equiv x^2+y^2-2x+4y+1=0$ is $P(a, b)$. If $C$ is the centre of the circle $S=0$,then $PC=$

The equation of the polar of the point $(1, 2)$ with respect to the circle $x^2 + y^2 = 7$ is: